I need help with this polynomial ....Its called division of polynomial

Question

Find the missing monomial .Assume that x is 0

?/3x^6=-15x^8


Divide .Assume that all variables are nonzero
15x^2-25x-40/5

 

 

Find the missing divided or divisor.Assumed that x is 0.

?/7x^5=-x^2-9x+1

 

 

 

 

Answer 1

? /3X⁶ = -15 X⁸

 

 

let the unknown be Q

 

   Q/ 3 X⁶  = -15 X⁸

 

    Now we have an equation where 2 fractions are equal:

      to solve we use  Cross Multiplication.

 

     Q = 3x⁶  * -15 X⁸  =  -45x¹⁴   is the answer, you can test it,

 

 ? / 7 X⁵ = - X² -9X + 1

 

 again let Q = ?, use cross multiplication.

 

     Q =  7 X⁵ * ( - X² - 9X  +1 ) = -7 X⁷  - 63 X⁶ + 7 X⁵

 

 

 

 What is dividend and divisor. The way you have written  only 40 should be divided by 5 which gives 8

 

 Probably it is ( 15 X² - 25X - 40 ) / 5 = 3X² - 5x - 8 

    

  

Answer 2

When doing division of polynomials, it's just like reducing a fraction or simplification.

 

1) n/3x^6 = -15x^8

 

    We need to multiply both sides of the equation by 3x^6

 

    ->  n/3x^6 * 3x^6 = -15x^8 * 3x^6    (* means multiplication)

 

    ->  n = -15x^8 * 3x^6

 

    ->  n = -45x^8x^6 = -45x^(8+6)        (add exponents, in this case)

 

    ->  n = -45x^14

 

 

2) 15x^2 - 25x - 40/5

 

    We can break this polynomial down like so...

 

    -> 15x^x/5 -25x/5 -40/5

 

    -> 3x^2 -5x - 8

 

 

3) n/7x^5 = -x^2-9x+1

 

    We can do the same as we did for #1.

 

    -> n/7x^5 * 7x^5 = -x^2-9x+1 * 7x^5

 

    -> n = (-x^2-9x+1) * (7x^5)

 

    -> n = -7x^7 - 63x^6 + 7x^5 

 

I hope this helps!

 

Rashonda J.